1
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
The tangent to the curve, y = xex2 passing through the point (1, e) also passes through the point
A
$$\left( {{4 \over 3},2e} \right)$$
B
(3, 6e)
C
(2, 3e)
D
$$\left( {{5 \over 3},2e} \right)$$
2
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
If  $${{dy} \over {dx}} + {3 \over {{{\cos }^2}x}}y = {1 \over {{{\cos }^2}x}},\,\,x \in \left( {{{ - \pi } \over 3},{\pi \over 3}} \right)$$  and  $$y\left( {{\pi \over 4}} \right) = {4 \over 3},$$  then  $$y\left( { - {\pi \over 4}} \right)$$   equals -
A
$${1 \over 3} + {e^6}$$
B
$${1 \over 3}$$
C
$${1 \over 3}$$ + e3
D
$$-$$ $${4 \over 3}$$
3
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
The shortest distance between the point  $$\left( {{3 \over 2},0} \right)$$   and the curve y = $$\sqrt x$$, (x > 0), is -
A
$${{\sqrt 3 } \over 2}$$
B
$${5 \over 4}$$
C
$${3 \over 2}$$
D
$${{\sqrt 5 } \over 2}$$
4
JEE Main 2018 (Online) 16th April Morning Slot
+4
-1
Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f(x) = 2x3 $$-$$ 9x2 + 12x + 5 in the interval [0, 3]. Then M $$-$$m is equal to :
A
5
B
9
C
4
D
1
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